Question

известно, что $\frac{sin a + 3 cos a}{sin a - cos a}$ = 3 чему равна cos2a

Answer 1

$\frac{ \sin(a) + 3 \cos(a) }{ \sin(a) - \cos(a) } = 3 \\ \\ 3(\sin(a) - \cos(a)) = \sin(a) + 3 \cos(a) \\ \\ 3 \sin(a) - 3 \cos(a) = \sin(a) + 3 \cos(a) \\ \\ 2 \sin(a) - 6 \cos(a) = 0 \\ \\ \sin(a) - 3 \cos(a) = 0$
Разделим на соsa : cosa ≠ 0

$tga - 3 = 0 \\ tga = 3$

Воспользуемся формулой:

${(tga)}^{2} + 1 = \frac{1}{ { (\cos(a)) }^{2} } \\ \\ \frac{1}{ { (\cos(a)) }^{2} } = 10 \\ \\ { (\cos(a) )}^{2} = \frac{1}{10}$

$\cos(2a) = 2 { (\cos(a) )}^{2} - 1 = 2 \times \frac{1}{10} - 1 = \\ \\ = \frac{1}{5} - 1 = 0.2 - 1 = - 0.8$


ОТВЕТ: -0,8